Advancements in the Multiscale Modeling of Blood Clot Formation

Blood clotting is a remarkably complex process that includes a number of different aspects, including chemical reactions, cellular morphological changes, and the binding and aggregation of a variety of molecules. Because of this complexity, this process is difficult to study in laboratory settings, and similarly difficult to model mathematically and computationally. Many efforts have been taken to model the different aspects of blood clotting. However, many aspects occur at different length and time scales, making one all-encompassing model nearly impossible to develop. To try and compensate for this, a multiscale approach is used that combines several submodels, each focused on different aspects of the clotting process. As is normally the case with applied mathematics, a compromise is made between fidelity and the complexity of the model. Once a model is developed, the work continues with improvements to the model in order to make it more realistically accurate, or improve its computational efficiency. In this thesis, I will present several advancements to the multiscale approach of the model. I will discuss improvements to the fibrin submodel that attempt to better capture the biological realities of this aspect of blood clotting. Additionally, I will discuss parallelization of the model, allowing for increased computation speed as further additions to the model are made. Lastly, I will present an entirely new method of representing the cellular submodel. These results show promise for the current and future state of multiscale modeling of blood clotting.